The aim of this paper is to determine the strain-rate-dependent mechanical behavior of living and fixed osteocytes and chondrocytes, in vitro. First, atomic force microscopy (AFM) was used to obtain the force–indentation curves of these single cells at four different strain-rates. These results were then employed in inverse finite element analysis (FEA) using modified standard neo-Hookean solid (MSnHS) idealization of these cells to determine their mechanical properties. In addition, a FEA model with a newly developed spring element was employed to accurately simulate AFM evaluation in this study. We report that both cytoskeleton (CSK) and intracellular fluid govern the strain-rate-dependent mechanical property of living cells whereas intracellular fluid plays a predominant role on fixed cells' behavior. In addition, through the comparisons, it can be concluded that osteocytes are stiffer than chondrocytes at all strain-rates tested indicating that the cells could be the biomarker of their tissue origin. Finally, we report that MSnHS is able to capture the strain-rate-dependent mechanical behavior of osteocyte and chondrocyte for both living and fixed cells. Therefore, we concluded that the MSnHS is a good model for exploration of mechanical deformation responses of single osteocytes and chondrocytes. This study could open a new avenue for analysis of mechanical behavior of osteocytes and chondrocytes as well as other similar types of cells.

References

References
1.
Jones
,
W. R.
,
Ting-Beall
,
H. P.
,
Lee
,
G. M.
,
Kelley
,
S. S.
,
Hochmuth
,
R. M.
, and
Guilak
,
F.
,
1997
, “
Mechanical Properties of Human Chondrocytes and Chondrons From Normal and Osteoarthritic Cartilage
,”
43rd Annual Meeting, Orthopaedic Research Society
, San Francisco, CA, pp.
199
234
.
2.
Trickey
,
W. R.
,
Lee
,
G. M.
, and
Guilak
,
F.
,
2000
, “
Viscoelastic Properties of Chondrocytes from Normal and Osteoarthritic Human Cartilage
,”
J. Orthop. Res.
,
18
(
6
), pp.
891
898
.10.1002/jor.1100180607
3.
Guilak
,
F.
,
Erickson
,
G. R.
, and
Ting-Beall
,
H. P.
,
2002
, “
The Effects of Osmotic Stress on the Viscoelastic and Physical Properties of Articular Chondrocytes
,”
Biophys. J.
,
82
(
2
), pp.
720
727
.10.1016/S0006-3495(02)75434-9
4.
Ofek
,
G.
,
Dowling
,
E.
,
Raphael
,
R.
,
McGarry
,
J.
, and
Athanasiou
,
K.
,
2010
, “
Biomechanics of Single Chondrocytes Under Direct Shear
,”
Biomech. Model. Mechanobiol.
,
9
(
2
), pp.
153
162
.10.1007/s10237-009-0166-1
5.
Wu
,
J. Z.
, and
Herzog
,
W.
,
2006
, “
Analysis of the Mechanical Behavior of Chondrocytes in Unconfined Compression Tests for Cyclic Loading
,”
J. Biomech.
,
39
(
4
), pp.
603
616
.10.1016/j.jbiomech.2005.01.007
6.
Moo
,
E. K.
,
Herzog
,
W.
,
Han
,
S. K.
,
Abu Osman
,
N. A.
,
Pingguan-Murphy
,
B.
, and
Federico
,
S.
,
2012
, “
Mechanical Behaviour of In-Situ Chondrocytes Subjected to Different Loading Rates: A Finite Element Study
,”
Biomech. Model. Mechanobiol.
,
11
(
7
), pp.
983
993
.10.1007/s10237-011-0367-2
7.
Oloyede
,
A.
,
Flachsmann
,
R.
, and
Broom
,
N. D.
,
1992
, “
The Dramatic Influence of Loading Velocity on the Compressive Response of Articular Cartilage
,”
Connect. Tissue Res.
,
27
(
4
), pp.
211
224
.10.3109/03008209209006997
8.
Ewers
,
B. J.
,
Dvoracek-Driksna
,
D.
,
Orth
,
M. W.
, and
Haut
,
R. C.
,
2001
, “
The Extent of Matrix Damage and Chondrocyte Death in Mechanically Traumatized Articular Cartilage Explants Depends on Rate of Loading
,”
J. Orthop. Res.
,
19
(
5
), pp.
779
784
.10.1016/S0736-0266(01)00006-7
9.
Kurz
,
B.
,
Jin
,
M.
,
Patwari
,
P.
,
Cheng
,
D. M.
,
Lark
,
M. W.
, and
Grodzinsky
,
A. J.
,
2001
, “
Biosynthetic Response and Mechanical Properties of Articular Cartilage After Injurious Compression
,”
J. Orthop. Res.
,
19
(
16
), pp.
1140
1146
.10.1016/S0736-0266(01)00033-X
10.
Quinn
,
T. M.
,
Allen
,
R. G.
,
Schalet
,
B. J.
,
Perumbuli
,
P.
, and
Hunziker
,
E. B.
,
2001
, “
Matrix and Cell Injury Due to Sub-Impact Loading of Adult Bovine Articular Cartilage Explants: Effects of Strain Rate and Peak Stress
,”
J. Orthop. Res.
,
19
(
2
), pp.
242
249
.10.1016/S0736-0266(00)00025-5
11.
Radin
,
E. L.
,
Paul
,
I. L.
, and
Lowy
,
M.
,
1970
, “
A Comparison of the Dynamic Force Transmitting Properties of Subchondral Bone and Articular Cartilage
,”
J. Bone Joint Surg.
,
52
(
3
), pp.
444
456
.
12.
Nguyen
,
T. D.
,
Gu
,
Y. T.
,
Oloyede
,
A.
, and
Senadeera
,
W.
,
2014
, “
Analysis of Strain-Rate-Dependent Mechanical Behavior of Single Chondrocyte: A Finite Element Study
,”
Int. J. Comput.Methods
,
11
(
1
), pp.
1
20
.10.1142/S0219876213020039
13.
Oloyede
,
A.
, and
Broom
,
N.
,
1993
, “
Stress-Sharing Between the Fluid and Solid Components of Articular Cartilage Under Varying Rates of Compression
,”
Connect. Tissue Res.
,
30
(
2
), pp.
127
141
.
14.
Oloyede
,
A.
, and
Broom
,
N. D.
,
1993
, “
A Physical Model for the Time-Dependent Deformation of Articular Cartilage
,”
Connect. Tissue Res.
,
29
(
4
), pp.
251
261
.10.3109/03008209309016831
15.
Moeendarbary
,
E.
,
Valon
,
L.
,
Fritzsche
,
M.
,
Harris
,
A. R.
,
Moulding
,
D. A.
,
Thrasher
,
A. J.
,
Stride
,
E.
,
Mahadevan
,
L.
, and
Charras
,
G. T.
,
2013
, “
The Cytoplasm of Living Cells Behaves as a Poroelastic Material
,”
Nat. Mater.
,
12
(3), pp.
253
261
.10.1038/nmat3517
16.
Lim
,
C. T.
,
Zhou
,
E. H.
, and
Quek
,
S. T.
,
2006
, “
Mechanical Models for Living Cells—A Review
,”
J. Biomech.
,
39
(
2
), pp.
195
216
.10.1016/j.jbiomech.2004.12.008
17.
Fung
,
Y. C.
,
1965
,
Foundations of Solid Mechanics
,
Prentice-Hall
,
Englewood Cliffs, NJ
.
18.
Darling
,
E. M.
,
Zauscher
,
S.
, and
Guilak
,
F.
,
2006
, “
Viscoelastic Properties of Zonal Articular Chondrocytes Measured by Atomic Force Microscopy
,”
Osteoarthritis Cartilage
,
14
(
6
), pp.
571
579
.10.1016/j.joca.2005.12.003
19.
Vaziri
,
A.
, and
Mofrad
,
M. R. K.
,
2007
, “
Mechanics and Deformation of the Nucleus in Micropipette Aspiration Experiment
,”
J. Biomech.
,
40
(
9
), pp.
2053
2062
.10.1016/j.jbiomech.2006.09.023
20.
Cheng
,
F.
,
Unnikrishnan
,
G. U.
, and
Reddy
,
J. N.
,
2010
, “
Micro-Constituent Based Viscoelastic Finite Element Analysis of Biological Cells
,”
Int. J. Appl. Mech.
,
2
(
2
), pp.
229
249
.10.1142/S1758825110000512
21.
Sato
,
M.
,
Theret
,
D. P.
,
Wheeler
,
L. T.
,
Ohshima
,
N.
, and
Nerem
,
R. M.
,
1990
, “
Application of the Micropipette Technique to the Measurement of Cultured Porcine Aortic Endothelial Cell Viscoelastic Properties
,”
ASME J. Biomech. Eng.
,
112
(
3
), pp.
263
268
.10.1115/1.2891183
22.
Guilak
,
F.
,
Tedrow
,
J. R.
, and
Burgkart
,
R.
,
2000
, “
Viscoelastic Properties of the Cell Nucleus
,”
Biochem. Biophys. Res. Commun.
,
269
(
3
), pp.
781
786
.10.1006/bbrc.2000.2360
23.
Guilak
,
F.
,
2000
, “
The Deformation Behavior and Viscoelastic Properties of Chondrocytes in Articular Cartilage
,”
Biorheology
,
37
(
1–2
), pp.
27
44
.
24.
Darling
,
E. M.
,
Zauscher
,
S.
,
Block
,
J. A.
, and
Guilak
,
F.
,
2007
, “
A Thin-Layer Model for Viscoelastic, Stress–Relaxation Testing of Cells Using Atomic Force Microscopy: Do Cell Properties Reflect Metastatic Potential
,”
Biophys. J.
,
92
(
5
), pp.
1784
1791
.10.1529/biophysj.106.083097
25.
Zhou
,
E. H.
,
Lim
,
C. T.
, and
Quek
,
S. T.
,
2005
, “
Finite Element Simulation of the Micropipette Aspiration of a Living Cell Undergoing Large Viscoelastic Deformation
,”
Mech. Adv. Mater. Struct.
,
12
(
6
), pp.
501
512
.10.1080/15376490500259335
26.
Touhami
,
A.
,
Nysten
,
B.
, and
Dufrene
,
Y. F.
,
2003
, “
Nanoscale Mapping of the Elasticity of Microbial Cells by Atomic Force Microscopy
,”
Langmuir
,
19
(
11
), pp.
4539
4543
.10.1021/la034136x
27.
Rico
,
F.
,
Roca-Cusachs
,
P.
,
Gavara
,
N.
,
Farre
,
R.
,
Rotger
,
M.
, and
Navajas
,
D.
,
2005
, “
Probing Mechanical Properties of Living Cells by Atomic Force Microscopy With Blunted Pyramidal Cantilever Tips
,”
Phys. Rev. E
,
72
(2), p.
021914
.10.1103/PhysRevE.72.021914
28.
Zhang
,
C. Y.
, and
Zhang
,
Y. W.
,
2007
, “
Effects of Membrane Pre-Stress and Intrinsic Viscoelasticity on Nanoindentation of Cells Using AFM
,”
Philos. Mag.
,
87
(
23
), pp.
3415
3435
.10.1080/14786430701288094
29.
Lin
,
D. C.
,
Dimitriadis
,
E. K.
, and
Horkay
,
F.
,
2007
, “
Elasticity of Rubber-Like Materials Measured by AFM Nanoindentation
,”
eXPRESS Polym. Lett.
,
1
(
9
), pp.
576
584
.10.3144/expresspolymlett.2007.79
30.
Kuznetsova
,
T. G.
,
Starodubtseva
,
M. N.
,
Yegorenkov
,
N. I.
,
Chizhik
,
S. A.
, and
Zhanov
,
R. I.
,
2007
, “
Atomic Force Microscopy Probing of Cell Elasticity
,”
Micron
,
38
(
8
), pp.
824
833
.10.1016/j.micron.2007.06.011
31.
Faria
,
E. C.
,
Ma
,
N.
,
Gazi
,
E.
,
Gardner
,
P.
,
Brown
,
M.
,
Clarke
,
N. W.
, and
Snook
,
R. D.
,
2008
, “
Measurement of Elastic Properties of Prostate Cancer Cells Using AFM
,”
Analyst
,
133
(
11
), pp.
1498
1500
.10.1039/b803355b
32.
Yusuf
,
K. Q.
,
Motta
,
N.
,
Pawlak
,
Z.
, and
Oloyede
,
A.
,
2012
, “
A Microanalytical Study of the Surfaces of Normal, Delipidized, and Artificially “Resurfaced” Articular Cartilage
,”
Connect. Tissue Res.
,
53
(
3
), pp.
236
245
.10.3109/03008207.2011.630764
33.
Ladjal
,
H.
,
Hanus
,
J. L.
,
Pillarisetti
,
A.
,
Keefer
,
C.
,
Ferreira
,
A.
, and
Desai
,
J. P.
,
2009
, “
Atomic Force Microscopy-Based Single-Cell Indentation: Experimentation and Finite Element Simulation
,”
IEEE/RSJ International Conference on Intelligent Robots and Systems
, St. Louis, MO, Oct. 10–15, pp.
1326
1332
.
34.
Svitkina
,
T.
,
2010
, “
Imaging Cytoskeleton Components by Electron Microscopy
,”
Cytoskeleton Methods and Protocols
,
Humana Press
,
New York
, pp.
187
206
.
35.
Lin
,
D. C.
,
Dimitriadis
,
E. K.
, and
Horkay
,
F.
,
2007
, “
Robust Strategies for Automated AFM Force Curve Analysis—I. Non-Adhesive Indentation of Soft, Inhomogeneous Materials
,”
ASME J. Biomech. Eng.
,
129
(
3
), pp.
430
440
.10.1115/1.2720924
36.
Brown
,
C. P.
,
Nguyen
,
T. C.
,
Moody
,
H. R.
,
Crawford
,
R. W.
, and
Oloyede
,
A.
,
2009
, “
Assessment of Common Hyperelastic Constitutive Equations for Describing Normal and Osteoarthritic Articular Cartilage
,”
Proc. Inst. Mech. Eng. H
,
223
(
6
), pp.
643
652
.10.1243/09544119JEIM546
37.
Lin
,
D. C.
,
Shreiber
,
D. I.
,
Dimitriadis
,
E. K.
, and
Horkay
,
F.
,
2009
, “
Spherical Indentation of Soft Matter Beyond the Hertzian Regime: Numerical and Experimental Validation of Hyperelastic Models
,”
Biomech. Model. Mechanobiol.
,
8
(
5
), pp.
345
358
.10.1007/s10237-008-0139-9
38.
Nguyen
,
T. D.
, and
Gu
,
Y. T.
,
2014
, “
Exploration of Mechanisms Underlying the Strain-Rate-Dependent Mechanical Property of Single Chondrocytes
,”
Appl. Phys. Lett.
,
104
(
18
), pp.
1
5
.10.1063/1.4876056
39.
Nguyen
,
B. V.
,
Wang
,
Q. G.
,
Kuiper
,
N. J.
,
Haj
,
A. J. E.
,
Thomas
,
C. R.
, and
Zhang
,
Z.
,
2010
, “
Biomechanical Properties of Single Chondrocytes and Chondrons Determined by Micromanipulation and Finite-Element Modelling
,”
J. R. Soc. Interface
,
7
(
53
), pp.
1723
1733
.10.1098/rsif.2010.0207
40.
Abaqus,
1996
,
Abaqus/Standard User's Manual (version 5.6)
,
Hibbitt, Karlsson, and Sorensen, Inc.
,
Pawtucket, RI
.
41.
Ritter
,
Z.
,
Staude
,
A.
,
Prohaska
,
S.
, and
Felsenberg
,
D.
,
2012
, “
Osteocytes Characterization Using Synchrotron Radiation CT and Finite Element Analysis
,”
Applied Biological Engineering—Principles and Practice
,
D. G. R.
Naik
, ed.,
InTech
,
Winchester, UK
.
42.
Verbruggen
,
S. W.
,
Vaughan
,
T. J.
, and
McNamara
,
L. M.
,
2012
, “
Strain Amplification in Bone Mechanobiology: A Computational Investigation of the in Vivo Mechanics of Osteocytes
,”
J. R. Soc. Interface
,
9
(
75
), pp.
2735
2744
.10.1098/rsif.2012.0286
43.
Trickey
,
W. R.
,
Baaijens
,
F. P. T.
,
Laursen
,
T. A.
,
Alexopoulos
,
L. G.
, and
Guilak
,
F.
,
2006
, “
Determination of the Poisson's Ratio of the Cell: Recovery Properties of Chondrocytes After Release From Complete Micropipette Aspiration
,”
J. Biomech.
,
39
(
1
), pp.
78
87
.10.1016/j.jbiomech.2004.11.006
44.
Yamane
,
Y.
,
Shiga
,
H.
,
Haga
,
H.
,
Kawabata
,
K.
,
Abe
,
K.
, and
Ito
,
E.
,
2000
, “
Quantitative Analyses of Topography and Elasticity of Living and Fixed Astrocytes
,”
J. Electron Microsc.
,
49
(
3
), pp.
463
471
.10.1093/oxfordjournals.jmicro.a023830
45.
Vegh
,
A. G.
,
Fazakas
,
C.
,
Nagy
,
K.
,
Wilhelm
,
I.
,
Krizbai
,
I. A.
,
Nagyőszi
,
P.
,
Szegletes
,
Z.
, and
Váró
,
G.
,
2011
, “
Spatial and Temporal Dependence of the Cerebral Endothelial Cells Elasticity
,”
J. Mol. Recognit.
,
24
(
3
), pp.
422
428
.10.1002/jmr.1107
46.
Lieleg
,
O.
,
Kayser
,
J.
,
Brambilla
,
G.
,
Cipelletti
,
L.
, and
Bausch
,
A. R.
,
2011
, “
Slow Dynamics and Internal Stress Relaxation in Bundled Cytoskeletal Networks
,”
Nat. Mater.
,
10
(
3
), pp.
236
242
.10.1038/nmat2939
47.
Darling
,
E. M.
,
Topel
,
M.
,
Zauscher
,
S.
,
Vail
,
T. P.
, and
Guilak
,
F.
,
2008
, “
Viscoelastic Properties of Human Mesenchymally-Derived Stem Cells and Primary Osteoblasts, Chondrocytes, and Adipocytes
,”
J. Biomech.
,
41
(
2
), pp.
454
464
.10.1016/j.jbiomech.2007.06.019
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